LMFDB - Embedded newform 460.2.o.a.159.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label			159.4
Character	$\chi$	$=$	460.159
Dual form			460.2.o.a.379.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18971 + 0.764582i) q^{2} +(0.0739958 + 0.514652i) q^{3} +(0.830830 + 1.81926i) q^{4} +(0.629973 - 2.14549i) q^{5} +(-0.305460 + 0.668863i) q^{6} +(0.858171 + 0.743609i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(2.61909 - 0.769034i) q^{9} +O(q^{10})$	\(q+(1.18971 + 0.764582i) q^{2} +(0.0739958 + 0.514652i) q^{3} +(0.830830 + 1.81926i) q^{4} +(0.629973 - 2.14549i) q^{5} +(-0.305460 + 0.668863i) q^{6} +(0.858171 + 0.743609i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(2.61909 - 0.769034i) q^{9} +(2.38989 - 2.07085i) q^{10} +(-0.874810 + 0.562206i) q^{12} +(0.452426 + 1.54082i) q^{14} +(1.15080 + 0.165460i) q^{15} +(-2.61944 + 3.02300i) q^{16} +(3.70395 + 1.08758i) q^{18} +(4.42662 - 0.636451i) q^{20} +(-0.319199 + 0.496683i) q^{21} +(-1.96963 + 4.37271i) q^{23} -1.47062 q^{24} +(-4.20627 - 2.70320i) q^{25} +(1.23756 + 2.70989i) q^{27} +(-0.639827 + 2.17905i) q^{28} +(1.34473 - 2.94454i) q^{29} +(1.24261 + 1.07673i) q^{30} +(-5.42771 + 1.59372i) q^{32} +(2.13603 - 1.37274i) q^{35} +(3.57509 + 4.12588i) q^{36} +(5.75302 + 2.62732i) q^{40} +(-10.7829 - 3.16615i) q^{41} +(-0.759509 + 0.346856i) q^{42} +(10.1596 - 1.46073i) q^{43} -6.10370i q^{45} +(-5.68658 + 3.69632i) q^{46} -12.1712 q^{47} +(-1.74962 - 1.12441i) q^{48} +(-0.812702 - 5.65246i) q^{49} +(-2.93743 - 6.43207i) q^{50} +(-0.599585 + 4.17020i) q^{54} +(-2.42727 + 2.10324i) q^{56} +(3.85118 - 2.47500i) q^{58} +(0.655102 + 2.23107i) q^{60} +(-1.68634 - 0.242459i) q^{61} +(2.81948 + 1.28762i) q^{63} +(-7.67594 - 2.25386i) q^{64} +(1.05385 - 1.63982i) q^{67} +(-2.39617 - 0.690111i) q^{69} +3.59084 q^{70} +(1.09876 + 7.64205i) q^{72} +(1.07996 - 2.36479i) q^{75} +(4.83564 + 7.52440i) q^{80} +(5.58593 - 3.58986i) q^{81} +(-10.4078 - 12.0112i) q^{82} +(-3.95775 - 13.4789i) q^{83} +(-1.16880 - 0.168048i) q^{84} +(13.2038 + 6.02999i) q^{86} +(1.61492 + 0.474182i) q^{87} +(18.1065 - 2.60331i) q^{89} +(4.66678 - 7.26165i) q^{90} +(-9.59153 + 0.0497018i) q^{92} +(-14.4803 - 9.30591i) q^{94} +(-1.22184 - 2.67545i) q^{96} +(3.35489 - 7.34618i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.18971	+	0.764582i	0.841254	+	0.540641i
$2$	1.18971	+	0.764582i	0.841254	+	0.540641i
$3$	0.0739958	+	0.514652i	0.0427215	+	0.297134i	0.999969	+	0.00786458i	$0.00250340\pi$
$3$	0.0739958	+	0.514652i	0.0427215	+	0.297134i	−0.957248	+	0.289270i	$0.906588\pi$
$4$	0.830830	+	1.81926i	0.415415	+	0.909632i
$5$	0.629973	−	2.14549i	0.281733	−	0.959493i
$5$	0.629973	−	2.14549i	0.281733	−	0.959493i
$6$	−0.305460	+	0.668863i	−0.124703	+	0.273062i
$7$	0.858171	+	0.743609i	0.324358	+	0.281058i	0.801784	−	0.597614i	$-0.203885\pi$
$7$	0.858171	+	0.743609i	0.324358	+	0.281058i	−0.477426	+	0.878672i	$0.658430\pi$
$8$	−0.402527	+	2.79964i	−0.142315	+	0.989821i
$9$	2.61909	−	0.769034i	0.873029	−	0.256345i
$10$	2.38989	−	2.07085i	0.755750	−	0.654861i
$11$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$11$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$12$	−0.874810	+	0.562206i	−0.252536	+	0.162295i
$13$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$13$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$14$	0.452426	+	1.54082i	0.120916	+	0.411802i
$15$	1.15080	+	0.165460i	0.297134	+	0.0427215i
$16$	−2.61944	+	3.02300i	−0.654861	+	0.755750i
$17$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$17$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$18$	3.70395	+	1.08758i	0.873029	+	0.256345i
$19$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$19$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$20$	4.42662	−	0.636451i	0.989821	−	0.142315i
$21$	−0.319199	+	0.496683i	−0.0696549	+	0.108385i
$22$		0			0
$23$	−1.96963	+	4.37271i	−0.410696	+	0.911772i
$23$	−1.96963	+	4.37271i	−0.410696	+	0.911772i
$24$	−1.47062			−0.300190
$25$	−4.20627	−	2.70320i	−0.841254	−	0.540641i
$26$		0			0
$27$	1.23756	+	2.70989i	0.238169	+	0.521518i
$28$	−0.639827	+	2.17905i	−0.120916	+	0.411802i
$29$	1.34473	−	2.94454i	0.249709	−	0.546787i	−0.742720	−	0.669602i	$-0.766465\pi$
$29$	1.34473	−	2.94454i	0.249709	−	0.546787i	0.992430	+	0.122815i	$0.0391921\pi$
$30$	1.24261	+	1.07673i	0.226868	+	0.196583i
$31$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$31$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$32$	−5.42771	+	1.59372i	−0.959493	+	0.281733i
$33$		0			0
$34$		0			0
$35$	2.13603	−	1.37274i	0.361055	−	0.232036i
$36$	3.57509	+	4.12588i	0.595849	+	0.687646i
$37$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$37$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$38$		0			0
$39$		0			0
$40$	5.75302	+	2.62732i	0.909632	+	0.415415i
$41$	−10.7829	−	3.16615i	−1.68401	−	0.494470i	−0.706919	−	0.707295i	$-0.749915\pi$
$41$	−10.7829	−	3.16615i	−1.68401	−	0.494470i	−0.977090	+	0.212825i	$0.931734\pi$
$42$	−0.759509	+	0.346856i	−0.117195	+	0.0535211i
$43$	10.1596	−	1.46073i	1.54932	−	0.222759i	0.686072	−	0.727533i	$-0.259333\pi$
$43$	10.1596	−	1.46073i	1.54932	−	0.222759i	0.863251	+	0.504774i	$0.168424\pi$
$44$		0			0
$45$		−	6.10370i		−	0.909886i
$46$	−5.68658	+	3.69632i	−0.838441	+	0.544993i
$47$	−12.1712			−1.77536			−0.887679	−	0.460462i	$-0.847684\pi$
$47$	−12.1712			−1.77536			−0.887679	+	0.460462i	$0.847684\pi$
$48$	−1.74962	−	1.12441i	−0.252536	−	0.162295i
$49$	−0.812702	−	5.65246i	−0.116100	−	0.807495i
$50$	−2.93743	−	6.43207i	−0.415415	−	0.909632i
$51$		0			0
$52$		0			0
$53$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$53$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$54$	−0.599585	+	4.17020i	−0.0815932	+	0.567493i
$55$		0			0
$56$	−2.42727	+	2.10324i	−0.324358	+	0.281058i
$57$		0			0
$58$	3.85118	−	2.47500i	0.505684	−	0.324983i
$59$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$59$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$60$	0.655102	+	2.23107i	0.0845733	+	0.288030i
$61$	−1.68634	−	0.242459i	−0.215913	−	0.0310437i	0.0335091	−	0.999438i	$-0.489332\pi$
$61$	−1.68634	−	0.242459i	−0.215913	−	0.0310437i	−0.249423	+	0.968395i	$0.580241\pi$
$62$		0			0
$63$	2.81948	+	1.28762i	0.355222	+	0.162224i
$64$	−7.67594	−	2.25386i	−0.959493	−	0.281733i
$65$		0			0
$66$		0			0
$67$	1.05385	−	1.63982i	0.128748	−	0.200336i	−0.770895	−	0.636963i	$-0.780190\pi$
$67$	1.05385	−	1.63982i	0.128748	−	0.200336i	0.899643	+	0.436626i	$0.143827\pi$
$68$		0			0
$69$	−2.39617	−	0.690111i	−0.288465	−	0.0830796i
$70$	3.59084			0.429187
$71$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$71$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$72$	1.09876	+	7.64205i	0.129490	+	0.900625i
$73$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$73$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$74$		0			0
$75$	1.07996	−	2.36479i	0.124703	−	0.273062i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$79$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$80$	4.83564	+	7.52440i	0.540641	+	0.841254i
$81$	5.58593	−	3.58986i	0.620659	−	0.398873i
$82$	−10.4078	−	12.0112i	−1.14935	−	1.32642i
$83$	−3.95775	−	13.4789i	−0.434419	−	1.47950i	−0.828274	−	0.560324i	$-0.810677\pi$
$83$	−3.95775	−	13.4789i	−0.434419	−	1.47950i	0.393855	−	0.919173i	$-0.371141\pi$
$84$	−1.16880	−	0.168048i	−0.127526	−	0.0183355i
$85$		0			0
$86$	13.2038	+	6.02999i	1.42381	+	0.650231i
$87$	1.61492	+	0.474182i	0.173137	+	0.0508377i
$88$		0			0
$89$	18.1065	−	2.60331i	1.91928	−	0.275951i	0.924765	−	0.380540i	$-0.124262\pi$
$89$	18.1065	−	2.60331i	1.91928	−	0.275951i	0.994516	+	0.104589i	$0.0333526\pi$
$90$	4.66678	−	7.26165i	0.491922	−	0.765445i
$91$		0			0
$92$	−9.59153	+	0.0497018i	−0.999987	+	0.00518177i
$93$		0			0
$94$	−14.4803	−	9.30591i	−1.49353	−	0.959831i
$95$		0			0
$96$	−1.22184	−	2.67545i	−0.124703	−	0.273062i
$97$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$97$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$98$	3.35489	−	7.34618i	0.338895	−	0.742076i
$99$		0			0
$100$	1.42315	−	9.89821i	0.142315	−	0.989821i
$101$	−6.03671	+	1.77254i	−0.600675	+	0.176374i	−0.567912	−	0.823089i	$-0.692249\pi$
$101$	−6.03671	+	1.77254i	−0.600675	+	0.176374i	−0.0327629	+	0.999463i	$0.510431\pi$
$102$		0			0
$103$	−6.26335	−	9.74596i	−0.617146	−	0.960298i	−0.999344	−	0.0362175i	$-0.988469\pi$
$103$	−6.26335	−	9.74596i	−0.617146	−	0.960298i	0.382198	−	0.924081i	$-0.375167\pi$
$104$		0			0
$105$	0.864543	+	0.997735i	0.0843707	+	0.0973690i
$106$		0			0
$107$	−14.1368	−	2.03256i	−1.36665	−	0.196495i	−0.580366	−	0.814356i	$-0.697090\pi$
$107$	−14.1368	−	2.03256i	−1.36665	−	0.196495i	−0.786287	+	0.617861i	$0.787999\pi$
$108$	−3.90179	+	4.50291i	−0.375450	+	0.433293i
$109$	18.1352	+	8.28207i	1.73704	+	0.793278i	0.991997	+	0.126258i	$0.0402968\pi$
$109$	18.1352	+	8.28207i	1.73704	+	0.793278i	0.745040	+	0.667020i	$0.232431\pi$
$110$		0			0
$111$		0			0
$112$	−4.49586	+	0.646407i	−0.424819	+	0.0610797i
$113$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$113$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$114$		0			0
$115$	8.14079	+	6.98051i	0.759133	+	0.650936i
$116$	6.47413			0.601108
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.926454	+	3.15521i	−0.0845733	+	0.288030i
$121$	−4.56957	+	10.0060i	−0.415415	+	0.909632i
$122$	−1.82088	−	1.57780i	−0.164854	−	0.142847i
$123$	0.831575	−	5.78373i	0.0749806	−	0.521502i
$124$		0			0
$125$	−8.44954	+	7.32157i	−0.755750	+	0.654861i
$126$	2.36989	+	3.68762i	0.211126	+	0.328519i
$127$	−18.9403	+	12.1722i	−1.68068	+	1.08011i	−0.815175	+	0.579215i	$0.803359\pi$
$127$	−18.9403	+	12.1722i	−1.68068	+	1.08011i	−0.865508	+	0.500894i	$0.833004\pi$
$128$	−7.40890	−	8.55033i	−0.654861	−	0.755750i
$129$	1.50353	+	5.12057i	0.132379	+	0.450841i
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$		0			0
$133$		0			0
$134$	2.50756	−	1.14516i	0.216620	−	0.0989270i
$135$	6.59367	−	0.948027i	0.567493	−	0.0815932i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	−2.32310	−	2.65310i	−0.197756	−	0.225847i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	4.27206	+	2.74549i	0.361055	+	0.232036i
$141$	−0.900621	−	6.26396i	−0.0758460	−	0.527520i
$142$		0			0
$143$		0			0
$144$	−4.53576	+	9.93194i	−0.377980	+	0.827661i
$145$	−5.47034	−	4.74008i	−0.454287	−	0.393642i
$146$		0			0
$147$	2.84891	−	0.836517i	0.234975	−	0.0689947i
$148$		0			0
$149$	5.97547	+	9.29801i	0.489529	+	0.761723i	0.994866	−	0.101200i	$-0.0322681\pi$
$149$	5.97547	+	9.29801i	0.489529	+	0.761723i	−0.505337	+	0.862922i	$0.668632\pi$
$150$	3.09292	−	1.98770i	0.252536	−	0.162295i
$151$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$151$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$157$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$158$		0			0
$159$		0			0
$160$			12.6491i			1.00000i
$161$	−4.94186	+	2.28789i	−0.389473	+	0.180311i
$162$	9.39039			0.737779
$163$	12.4911	+	8.02754i	0.978378	+	0.628765i	0.929025	−	0.370016i	$-0.120648\pi$
$163$	12.4911	+	8.02754i	0.978378	+	0.628765i	0.0493527	+	0.998781i	$0.484284\pi$
$164$	−3.19871	−	22.2475i	−0.249777	−	1.73724i
$165$		0			0
$166$	5.59710	−	19.0620i	0.434419	−	1.47950i
$167$	0.564020	−	1.23503i	0.0436452	−	0.0955697i	−0.886553	−	0.462626i	$-0.846907\pi$
$167$	0.564020	−	1.23503i	0.0436452	−	0.0955697i	0.930199	+	0.367057i	$0.119634\pi$
$168$	−1.26205	−	1.09357i	−0.0973690	−	0.0843707i
$169$	−1.85009	+	12.8677i	−0.142315	+	0.989821i
$170$		0			0
$171$		0			0
$172$	11.0983	+	17.2694i	0.846241	+	1.31678i
$173$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$173$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$174$	1.55873	+	1.79888i	0.118167	+	0.136372i
$175$	−1.59957	−	5.44763i	−0.120916	−	0.411802i
$176$		0			0
$177$		0			0
$178$	23.5319	+	10.7467i	1.76379	+	0.805497i
$179$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$179$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$180$	11.1042	−	5.07114i	0.827661	−	0.377980i
$181$	−5.73933	+	0.825191i	−0.426601	+	0.0613360i	−0.352272	−	0.935898i	$-0.614591\pi$
$181$	−5.73933	+	0.825191i	−0.426601	+	0.0613360i	−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		−	0.885818i		−	0.0654815i
$184$	−11.4492	−	7.27438i	−0.844044	−	0.536274i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−10.1122	−	22.1427i	−0.737511	−	1.61492i
$189$	−0.953056	+	3.24581i	−0.0693246	+	0.236098i
$190$		0			0
$191$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$191$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$192$	0.591966	−	4.11722i	0.0427215	−	0.297134i
$193$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$193$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$194$		0			0
$195$		0			0
$196$	9.60811	−	6.17475i	0.686293	−	0.441054i
$197$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$197$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$198$		0			0
$199$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$199$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$200$	9.26113	−	10.6879i	0.654861	−	0.755750i
$201$	0.921919	+	0.421026i	0.0650271	+	0.0296969i
$202$	−8.53720	−	2.50675i	−0.600675	−	0.176374i
$203$	3.34359	−	1.52697i	0.234674	−	0.107172i
$204$		0			0
$205$	−13.5859	+	21.1401i	−0.948880	+	1.47649i
$206$		−	16.3837i		−	1.14151i
$207$	−1.79587	+	12.9672i	−0.124822	+	0.901284i
$208$		0			0
$209$		0			0
$210$	0.265707	+	1.84803i	0.0183355	+	0.127526i
$211$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$211$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$212$		0			0
$213$		0			0
$214$	−15.2646	−	13.2269i	−1.04347	−	0.904171i
$215$	3.26629	−	22.7175i	0.222759	−	1.54932i
$216$	−8.08486	+	2.37393i	−0.550105	+	0.161525i
$217$		0			0
$218$	15.2434	+	23.7191i	1.03241	+	1.60646i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−6.19543	+	7.14991i	−0.414877	+	0.478793i	−0.924269	−	0.381741i	$-0.875325\pi$
$223$	−6.19543	+	7.14991i	−0.414877	+	0.478793i	0.509393	+	0.860534i	$0.329870\pi$
$224$	−5.84301	−	2.66841i	−0.390402	−	0.178291i
$225$	−13.0954	−	3.84517i	−0.873029	−	0.256345i
$226$		0			0
$227$	24.2691	−	3.48937i	1.61080	−	0.231597i	0.722668	−	0.691195i	$-0.242916\pi$
$227$	24.2691	−	3.48937i	1.61080	−	0.231597i	0.888127	+	0.459598i	$0.152006\pi$
$228$		0			0
$229$			15.0042i			0.991507i	0.868463	+	0.495754i	$0.165108\pi$
$229$			15.0042i			0.991507i	−0.868463	+	0.495754i	$0.834892\pi$
$230$	4.34803	+	14.5291i	0.286701	+	0.958020i
$231$		0			0
$232$	7.70235	+	4.95000i	0.505684	+	0.324983i
$233$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$233$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$234$		0			0
$235$	−7.66756	+	26.1133i	−0.500176	+	1.70344i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$239$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$240$	−3.51463	+	3.04544i	−0.226868	+	0.196583i
$241$	16.1905	+	25.1929i	1.04292	+	1.62282i	0.743549	+	0.668682i	$0.233141\pi$
$241$	16.1905	+	25.1929i	1.04292	+	1.62282i	0.299373	+	0.954136i	$0.403223\pi$
$242$	−13.0868	+	8.41040i	−0.841254	+	0.540641i
$243$	8.11355	+	9.36354i	0.520485	+	0.600671i
$244$	−0.959964	−	3.26934i	−0.0614554	−	0.209298i
$245$	−12.6393	−	1.81726i	−0.807495	−	0.116100i
$246$	5.41147	−	6.24517i	0.345023	−	0.398177i
$247$		0			0
$248$		0			0
$249$	6.64406	−	3.03424i	0.421050	−	0.192287i
$250$	−15.6505	+	2.25020i	−0.989821	+	0.142315i
$251$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$251$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$252$			6.19918i			0.390511i
$253$		0			0
$254$	−31.8402			−1.99783
$255$		0			0
$256$	−2.27704	−	15.8371i	−0.142315	−	0.989821i
$257$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$257$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$258$	−2.12632	+	7.24158i	−0.132379	+	0.450841i
$259$		0			0
$260$		0			0
$261$	1.25751	−	8.74614i	0.0778376	−	0.541373i
$262$		0			0
$263$	−19.6294	+	17.0090i	−1.21040	+	1.04882i	−0.212981	+	0.977056i	$0.568317\pi$
$263$	−19.6294	+	17.0090i	−1.21040	+	1.04882i	−0.997422	+	0.0717640i	$0.977137\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.67960	+	9.12589i	0.163989	+	0.558495i
$268$	3.85884	+	0.554818i	0.235716	+	0.0338909i
$269$	16.7308	−	19.3084i	1.02009	−	1.17725i	0.0360466	−	0.999350i	$-0.488524\pi$
$269$	16.7308	−	19.3084i	1.02009	−	1.17725i	0.984048	−	0.177902i	$-0.0569310\pi$
$270$	8.56942	+	3.91352i	0.521518	+	0.238169i
$271$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$271$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.735312	−	4.93262i	−0.0442606	−	0.296909i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	2.98338	+	6.53268i	0.178291	+	0.390402i
$281$	6.73908	−	22.9512i	0.402020	−	1.36915i	−0.471286	−	0.881981i	$-0.656210\pi$
$281$	6.73908	−	22.9512i	0.402020	−	1.36915i	0.873305	−	0.487173i	$-0.161972\pi$
$282$	3.71783	−	8.14090i	0.221393	−	0.484784i
$283$	22.1870	+	19.2251i	1.31888	+	1.14282i	0.979339	+	0.202225i	$0.0648171\pi$
$283$	22.1870	+	19.2251i	1.31888	+	1.14282i	0.339541	+	0.940591i	$0.389728\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.89921	−	10.7354i	−0.407247	−	0.633689i
$288$	−12.9900	+	8.34818i	−0.765445	+	0.491922i
$289$	11.1326	+	12.8477i	0.654861	+	0.755750i
$290$	−2.88396	−	9.82185i	−0.169352	−	0.576759i
$291$		0			0
$292$		0			0
$293$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$293$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$294$	4.02897	+	1.18301i	0.234975	+	0.0689947i
$295$		0			0
$296$		0			0
$297$		0			0
$298$			15.6307i			0.905461i
$299$		0			0
$300$	5.19944			0.300190
$301$	9.80488	+	6.30121i	0.565144	+	0.363196i
$302$		0			0
$303$	−1.35893	−	2.97565i	−0.0780686	−	0.170946i
$304$		0			0
$305$	−1.58254	+	3.46528i	−0.0906160	+	0.198421i
$306$		0			0
$307$	3.34589	−	23.2711i	0.190960	−	1.32815i	−0.638515	−	0.769610i	$-0.720451\pi$
$307$	3.34589	−	23.2711i	0.190960	−	1.32815i	0.829474	−	0.558545i	$-0.188640\pi$
$308$		0			0
$309$	4.55232	−	3.94460i	0.258972	−	0.224401i
$310$		0			0
$311$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$311$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$312$		0			0
$313$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$313$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$314$		0			0
$315$	4.53877	−	5.23802i	0.255731	−	0.295129i
$316$		0			0
$317$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$317$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$318$		0			0
$319$		0			0
$320$	−9.67128	+	15.0488i	−0.540641	+	0.841254i
$321$		−	7.42592i		−	0.414474i
$322$	−7.62867	−	1.05652i	−0.425129	−	0.0588776i
$323$		0			0
$324$	11.1719	+	7.17972i	0.620659	+	0.398873i
$325$		0			0
$326$	8.72310	+	19.1009i	0.483128	+	1.05790i
$327$	−2.92045	+	9.94615i	−0.161501	+	0.550024i
$328$	13.2045	−	28.9138i	0.729096	−	1.59650i
$329$	−10.4450	−	9.05065i	−0.575852	−	0.498978i
$330$		0			0
$331$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$331$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$332$	21.2334	−	18.3988i	1.16533	−	1.00977i
$333$		0			0
$334$	1.61530	−	1.03809i	0.0883855	−	0.0568019i
$335$	−2.85433	−	3.29407i	−0.155949	−	0.179974i
$336$	−0.665349	−	2.26597i	−0.0362978	−	0.123619i
$337$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$337$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$338$	−12.0395	+	13.8943i	−0.654861	+	0.755750i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	7.80315	−	12.1419i	0.421331	−	0.655603i
$344$			29.0312i			1.56526i
$345$	−2.99015	+	4.70620i	−0.160984	+	0.253373i
$346$		0			0
$347$	26.5771	+	17.0801i	1.42673	+	0.916907i	0.999921	+	0.0125674i	$0.00400045\pi$
$347$	26.5771	+	17.0801i	1.42673	+	0.916907i	0.426814	+	0.904339i	$0.359636\pi$
$348$	0.479058	+	3.33192i	0.0256802	+	0.178610i
$349$	15.4972	+	33.9341i	0.829544	+	1.81645i	0.465356	+	0.885124i	$0.345926\pi$
$349$	15.4972	+	33.9341i	0.829544	+	1.81645i	0.364188	+	0.931325i	$0.381346\pi$
$350$	2.26213	−	7.70411i	0.120916	−	0.411802i
$351$		0			0
$352$		0			0
$353$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$353$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$354$		0			0
$355$		0			0
$356$	19.7795	+	30.7775i	1.04831	+	1.63120i
$357$		0			0
$358$		0			0
$359$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$359$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$360$	17.0882	+	2.45691i	0.900625	+	0.129490i
$361$	12.4424	−	14.3592i	0.654861	−	0.755750i
$362$	−7.45908	−	3.40645i	−0.392040	−	0.179039i
$363$	−5.48771	−	1.61134i	−0.288030	−	0.0845733i
$364$		0			0
$365$		0			0
$366$	0.677280	−	1.05387i	0.0354020	−	0.0550866i
$367$		−	38.2451i		−	1.99638i	−0.0601346	−	0.998190i	$-0.519153\pi$
$367$		−	38.2451i		−	1.99638i	0.0601346	−	0.998190i	$-0.480847\pi$
$368$	−8.05936	−	17.4082i	−0.420123	−	0.907467i
$369$	−30.6763			−1.59694
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$373$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$374$		0			0
$375$	−4.39329	−	3.80681i	−0.226868	−	0.196583i
$376$	4.89926	−	34.0751i	0.252660	−	1.75729i
$377$		0			0
$378$	−3.61555	+	3.13289i	−0.185964	+	0.161138i
$379$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$379$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$380$		0			0
$381$	−7.66596	−	8.84699i	−0.392739	−	0.453245i
$382$		0			0
$383$	−38.5483	−	5.54241i	−1.96973	−	0.283204i	−0.999090	−	0.0426504i	$-0.986420\pi$
$383$	−38.5483	−	5.54241i	−1.96973	−	0.283204i	−0.970636	−	0.240553i	$-0.922671\pi$
$384$	3.85222	−	4.44569i	0.196583	−	0.226868i
$385$		0			0
$386$		0			0
$387$	25.4855	−	11.6388i	1.29550	−	0.591636i
$388$		0			0
$389$	7.22297	−	11.2392i	0.366219	−	0.569848i	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	7.22297	−	11.2392i	0.366219	−	0.569848i	0.974643	+	0.223764i	$0.0718344\pi$
$390$		0			0
$391$		0			0
$392$	16.1520			0.815798
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$397$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$398$		0			0
$399$		0			0
$400$	19.1899	−	5.63465i	0.959493	−	0.281733i
$401$	−17.3130	+	15.0018i	−0.864571	+	0.749155i	−0.969439	−	0.245331i	$-0.921103\pi$
$401$	−17.3130	+	15.0018i	−0.864571	+	0.749155i	0.104869	+	0.994486i	$0.466558\pi$
$402$	0.774909	+	1.20578i	0.0386489	+	0.0601389i
$403$		0			0
$404$	−8.24020	−	9.50970i	−0.409965	−	0.473125i
$405$	−4.18303	−	14.2461i	−0.207856	−	0.707893i
$406$	5.14540	+	0.739797i	0.255362	+	0.0367155i
$407$		0			0
$408$		0			0
$409$	7.19768	+	2.11343i	0.355902	+	0.104502i	0.454796	−	0.890596i	$-0.349712\pi$
$409$	7.19768	+	2.11343i	0.355902	+	0.104502i	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	−32.3266	+	14.7631i	−1.59650	+	0.729096i
$411$		0			0
$412$	12.5267	−	19.4919i	0.617146	−	0.960298i
$413$		0			0
$414$	−12.0511	+	14.0542i	−0.592277	+	0.690724i
$415$	−31.4120			−1.54196
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$419$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$420$	−1.09686	+	2.40178i	−0.0535211	+	0.117195i
$421$	−15.3505	−	13.3013i	−0.748138	−	0.648265i	0.194948	−	0.980814i	$-0.437546\pi$
$421$	−15.3505	−	13.3013i	−0.748138	−	0.648265i	−0.943086	+	0.332548i	$0.892092\pi$
$422$		0			0
$423$	−31.8776	+	9.36010i	−1.54994	+	0.455103i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.26687	−	1.46205i	−0.0613082	−	0.0707534i
$428$	−8.04749	−	27.4072i	−0.388990	−	1.32478i
$429$		0			0
$430$	21.2554	−	24.5300i	1.02502	−	1.18294i
$431$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$431$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$432$	−11.4337	−	3.35724i	−0.550105	−	0.161525i
$433$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$433$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$434$		0			0
$435$	2.03471	−	3.16607i	0.0975568	−	0.151801i
$436$			39.8737i			1.90960i
$437$		0			0
$438$		0			0
$439$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$439$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$440$		0			0
$441$	−6.47547	−	14.1793i	−0.308356	−	0.675205i
$442$		0			0
$443$	−10.6623	+	23.3472i	−0.506581	+	1.10926i	0.467693	+	0.883891i	$0.345085\pi$
$443$	−10.6623	+	23.3472i	−0.506581	+	1.10926i	−0.974274	+	0.225367i	$0.927642\pi$
$444$		0			0
$445$	5.82119	−	40.4873i	0.275951	−	1.91928i
$446$	−12.8375	+	3.76942i	−0.607872	+	0.178487i
$447$	−4.34308	+	3.76330i	−0.205421	+	0.177998i
$448$	−4.91128	−	7.64210i	−0.232036	−	0.361055i
$449$	35.6475	−	22.9092i	1.68231	−	1.08115i	0.832835	−	0.553521i	$-0.186716\pi$
$449$	35.6475	−	22.9092i	1.68231	−	1.08115i	0.849473	−	0.527633i	$-0.176920\pi$
$450$	−12.6399	−	14.5872i	−0.595849	−	0.687646i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	31.5411	+	14.4043i	1.48030	+	0.676029i
$455$		0			0
$456$		0			0
$457$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$457$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$458$	−11.4720	+	17.8507i	−0.536049	+	0.834109i
$459$		0			0
$460$	−5.93577	+	20.6099i	−0.276757	+	0.960940i
$461$	−40.1683			−1.87082			−0.935412	−	0.353560i	$-0.884971\pi$
$461$	−40.1683			−1.87082			−0.935412	+	0.353560i	$0.884971\pi$
$462$		0			0
$463$	−5.60772	−	39.0025i	−0.260613	−	1.81260i	−0.528259	−	0.849083i	$-0.677155\pi$
$463$	−5.60772	−	39.0025i	−0.260613	−	1.81260i	0.267646	−	0.963517i	$-0.413754\pi$
$464$	5.37890	+	11.7782i	0.249709	+	0.546787i
$465$		0			0
$466$		0			0
$467$	−21.5090	−	18.6377i	−0.995318	−	0.862448i	−0.00482209	−	0.999988i	$-0.501535\pi$
$467$	−21.5090	−	18.6377i	−0.995318	−	0.862448i	−0.990496	+	0.137540i	$0.956080\pi$
$468$		0			0
$469$	2.12377	−	0.623595i	0.0980666	−	0.0287950i
$470$	−29.0879	+	25.2048i	−1.34173	+	1.16261i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$479$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$480$	−6.50989	+	0.935981i	−0.297134	+	0.0427215i
$481$		0			0
$482$			42.3513i			1.92905i
$483$	−1.54315	−	2.37404i	−0.0702156	−	0.108023i
$484$	−22.0000			−1.00000
$485$		0			0
$486$	2.49360	+	17.3434i	0.113112	+	0.786712i
$487$	3.43790	+	7.52795i	0.155786	+	0.341124i	0.971391	−	0.237485i	$-0.0763230\pi$
$487$	3.43790	+	7.52795i	0.155786	+	0.341124i	−0.815605	+	0.578609i	$0.803596\pi$
$488$	1.35759	−	4.62354i	0.0614554	−	0.209298i
$489$	−3.20710	+	7.02257i	−0.145030	+	0.317572i
$490$	−13.6477	−	11.8258i	−0.616539	−	0.534234i
$491$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$491$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$492$	11.2130	−	3.29244i	0.505523	−	0.148435i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	10.2244	+	1.47005i	0.458168	+	0.0658747i
$499$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$499$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$500$	−20.3400	−	9.28896i	−0.909632	−	0.415415i
$501$	0.677347	+	0.198887i	0.0302616	+	0.00888562i
$502$		0			0
$503$	31.3604	−	4.50894i	1.39829	−	0.201044i	0.598403	−	0.801195i	$-0.295802\pi$
$503$	31.3604	−	4.50894i	1.39829	−	0.201044i	0.799887	+	0.600151i	$0.204893\pi$
$504$	−4.73978	+	7.37523i	−0.211126	+	0.328519i
$505$			14.0684i			0.626034i
$506$		0			0
$507$	−6.75927			−0.300190
$508$	−37.8807	−	24.3444i	−1.68068	−	1.08011i
$509$	−5.43465	−	37.7988i	−0.240886	−	1.67540i	−0.647703	−	0.761893i	$-0.724270\pi$
$509$	−5.43465	−	37.7988i	−0.240886	−	1.67540i	0.406817	−	0.913510i	$-0.366639\pi$
$510$		0			0
$511$		0			0
$512$	9.39977	−	20.5826i	0.415415	−	0.909632i
$513$		0			0
$514$		0			0
$515$	−24.8556	+	7.29827i	−1.09527	+	0.321600i
$516$	−8.06648	+	6.98965i	−0.355107	+	0.307702i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.27690	−	0.758704i	−0.231185	−	0.0332394i	0.0257485	−	0.999668i	$-0.491803\pi$
$521$	−5.27690	−	0.758704i	−0.231185	−	0.0332394i	−0.256934	+	0.966429i	$0.582712\pi$
$522$	8.18321	−	9.44393i	0.358169	−	0.413349i
$523$	31.2428	+	14.2681i	1.36615	+	0.623901i	0.957405	−	0.288747i	$-0.0932387\pi$
$523$	31.2428	+	14.2681i	1.36615	+	0.623901i	0.408746	+	0.912648i	$0.365966\pi$
$524$		0			0
$525$	2.68527	−	1.22632i	0.117195	−	0.0535211i
$526$	−36.3582	+	5.22751i	−1.58529	+	0.227930i
$527$		0			0
$528$		0			0
$529$	−15.2411	−	17.2252i	−0.662658	−	0.748922i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−3.78953	+	12.9060i	−0.163989	+	0.558495i
$535$	−13.2666	+	29.0499i	−0.573566	+	1.25593i
$536$	4.16671	+	3.61047i	0.179974	+	0.155949i
$537$		0			0
$538$	34.6677	−	10.1793i	1.49463	−	0.438863i
$539$		0			0
$540$	7.20293	+	11.2080i	0.309965	+	0.482315i
$541$	26.8929	−	17.2830i	1.15622	−	0.743055i	0.185349	−	0.982673i	$-0.440658\pi$
$541$	26.8929	−	17.2830i	1.15622	−	0.743055i	0.970867	+	0.239618i	$0.0770221\pi$
$542$		0			0
$543$	−0.849373	−	2.89270i	−0.0364501	−	0.124138i
$544$		0			0
$545$	29.1938	−	33.6914i	1.25052	−	1.44318i
$546$		0			0
$547$	43.8196	+	12.8666i	1.87359	+	0.550136i	0.997712	+	0.0676046i	$0.0215356\pi$
$547$	43.8196	+	12.8666i	1.87359	+	0.550136i	0.875879	+	0.482531i	$0.160283\pi$
$548$		0			0
$549$	−4.60313	+	0.661829i	−0.196457	+	0.0282462i
$550$		0			0
$551$		0			0
$552$	2.89658	−	6.43061i	0.123287	−	0.273705i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$557$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$558$		0			0
$559$		0			0
$560$	−1.44541	+	10.0530i	−0.0610797	+	0.424819i
$561$		0			0
$562$	25.5656	−	22.1527i	1.07842	−	0.934457i
$563$	−17.3716	−	27.0308i	−0.732127	−	1.13921i	−0.985141	−	0.171749i	$-0.945058\pi$
$563$	−17.3716	−	27.0308i	−0.732127	−	1.13921i	0.253014	−	0.967463i	$-0.418578\pi$
$564$	10.6475	−	6.84275i	0.448342	−	0.288132i
$565$		0			0
$566$	11.6969	+	39.8361i	0.491659	+	1.67444i
$567$	7.46313	+	1.07304i	0.313422	+	0.0450633i
$568$		0			0
$569$	−28.3609	−	12.9520i	−1.18895	−	0.542975i	−0.280048	−	0.959986i	$-0.590351\pi$
$569$	−28.3609	−	12.9520i	−1.18895	−	0.542975i	−0.908902	+	0.417011i	$0.863078\pi$
$570$		0			0
$571$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$571$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$572$		0			0
$573$		0			0
$574$		−	18.0470i		−	0.753268i
$575$	20.1051	−	13.0685i	0.838441	−	0.544993i
$576$	−21.8373			−0.909886
$577$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$577$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$578$	3.42148	+	23.7969i	0.142315	+	0.989821i
$579$		0			0
$580$	4.07853	−	13.8902i	0.169352	−	0.576759i
$581$	6.62657	−	14.5102i	0.274917	−	0.601983i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	39.7577	−	25.5507i	1.64097	−	1.05459i	0.701104	−	0.713059i	$-0.252691\pi$
$587$	39.7577	−	25.5507i	1.64097	−	1.05459i	0.939870	−	0.341532i	$-0.110946\pi$
$588$	3.88881	+	4.48792i	0.160372	+	0.185079i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$593$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$594$		0			0
$595$		0			0
$596$	−11.9509	+	18.5960i	−0.489529	+	0.761723i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	6.18584	+	3.97540i	0.252536	+	0.162295i
$601$	6.44906	+	44.8542i	0.263063	+	1.82964i	0.509485	+	0.860479i	$0.329836\pi$
$601$	6.44906	+	44.8542i	0.263063	+	1.82964i	−0.246422	+	0.969163i	$0.579255\pi$
$602$	6.84719	+	14.9933i	0.279071	+	0.611079i
$603$	1.49905	−	5.10529i	0.0610459	−	0.207903i
$604$		0			0
$605$	18.5890	+	16.1074i	0.755750	+	0.654861i
$606$	0.658386	−	4.57918i	0.0267451	−	0.186016i
$607$	−32.4017	+	9.51399i	−1.31514	+	0.386161i	−0.862738	−	0.505652i	$-0.831252\pi$
$607$	−32.4017	+	9.51399i	−1.31514	+	0.386161i	−0.452405	+	0.891812i	$0.649434\pi$
$608$		0			0
$609$	1.03327	+	1.60780i	0.0418701	+	0.0651512i
$610$	−4.53226	+	2.91271i	−0.183506	+	0.117932i
$611$		0			0
$612$		0			0
$613$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$613$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$614$	21.7733	−	25.1278i	0.878700	−	1.01407i
$615$	−11.8851	−	5.42773i	−0.479253	−	0.218867i
$616$		0			0
$617$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$617$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$618$	8.43192	−	1.21233i	0.339181	−	0.0487669i
$619$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$619$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$620$		0			0
$621$	−14.2871	+	0.0740334i	−0.573321	+	0.00297086i
$622$		0			0
$623$	17.4743	+	11.2300i	0.700092	+	0.449922i
$624$		0			0
$625$	10.3854	+	22.7408i	0.415415	+	0.909632i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	9.40472	−	2.76147i	0.374693	−	0.110020i
$631$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$631$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.1835	+	48.3045i	0.562854	+	1.91691i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−23.0121	+	10.5093i	−0.909632	+	0.415415i
$641$	−43.3740	+	6.23624i	−1.71317	+	0.246317i	−0.927898	−	0.372834i	$-0.878386\pi$
$641$	−43.3740	+	6.23624i	−1.71317	+	0.246317i	−0.785272	+	0.619151i	$0.787477\pi$
$642$	5.67772	−	8.83470i	0.224082	−	0.348678i
$643$		−	44.0922i		−	1.73883i	−0.494084	−	0.869414i	$-0.664497\pi$
$643$		−	44.0922i		−	1.73883i	0.494084	−	0.869414i	$-0.335503\pi$
$644$	−8.26813	−	7.08970i	−0.325810	−	0.279373i
$645$	11.9333			0.469874
$646$		0			0
$647$	7.05423	+	49.0633i	0.277330	+	1.92888i	0.361390	+	0.932415i	$0.382302\pi$
$647$	7.05423	+	49.0633i	0.277330	+	1.92888i	−0.0840596	+	0.996461i	$0.526789\pi$
$648$	7.80182	+	17.0836i	0.306484	+	0.671107i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−4.22624	+	29.3941i	−0.165512	+	1.15116i
$653$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$653$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$654$	−11.0791	+	9.60013i	−0.433229	+	0.375395i
$655$		0			0
$656$	37.8165	−	24.3032i	1.47649	−	0.948880i
$657$		0			0
$658$	−5.50659	−	18.7537i	−0.214669	−	0.731096i
$659$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$659$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$660$		0			0
$661$	43.3297	+	19.7880i	1.68533	+	0.769664i	0.999106	+	0.0422726i	$0.0134598\pi$
$661$	43.3297	+	19.7880i	1.68533	+	0.769664i	0.686223	+	0.727391i	$0.259267\pi$
$662$		0			0
$663$		0			0
$664$	39.3290	−	5.65466i	1.52626	−	0.219443i
$665$		0			0
$666$		0			0
$667$	10.2270	+	11.6797i	0.395991	+	0.452241i
$668$	2.71545			0.105064
$669$	−4.13815	−	2.65943i	−0.159990	−	0.102819i
$670$	−0.877244	−	6.10136i	−0.0338909	−	0.235716i
$671$		0			0
$672$	0.940946	−	3.20457i	0.0362978	−	0.123619i
$673$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$673$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$674$		0			0
$675$	2.11985	−	14.7439i	0.0815932	−	0.567493i
$676$	−24.9468	+	7.32505i	−0.959493	+	0.281733i
$677$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$677$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	3.59162	+	12.2319i	0.137631	+	0.468728i
$682$		0			0
$683$	−32.8861	+	37.9526i	−1.25835	+	1.45222i	−0.419595	+	0.907711i	$0.637828\pi$
$683$	−32.8861	+	37.9526i	−1.25835	+	1.45222i	−0.838757	+	0.544505i	$0.816717\pi$
$684$		0			0
$685$		0			0
$686$	18.5670	−	8.47927i	0.708892	−	0.323740i
$687$	−7.72196	+	1.11025i	−0.294611	+	0.0423587i
$688$	−22.1967	+	34.5387i	−0.846241	+	1.31678i
$689$		0			0
$690$	−7.15569	+	3.31281i	−0.272413	+	0.126117i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	18.5600	+	40.6408i	0.704529	+	1.54270i
$695$		0			0
$696$	−1.97759	+	4.33031i	−0.0749602	+	0.164140i
$697$		0			0
$698$	−7.50819	+	52.2206i	−0.284189	+	1.97658i
$699$		0			0
$700$	8.58171	−	7.43609i	0.324358	−	0.281058i
$701$	28.6276	+	44.5455i	1.08125	+	1.68246i	0.546981	+	0.837145i	$0.315777\pi$
$701$	28.6276	+	44.5455i	1.08125	+	1.68246i	0.534270	+	0.845314i	$0.320587\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−14.0066	−	2.01385i	−0.527520	−	0.0758460i
$706$		0			0
$707$	−6.49860	−	2.96781i	−0.244405	−	0.111616i
$708$		0			0
$709$	−24.4080	+	11.1468i	−0.916661	+	0.418625i	−0.817159	−	0.576412i	$-0.804452\pi$
$709$	−24.4080	+	11.1468i	−0.916661	+	0.418625i	−0.0995021	+	0.995037i	$0.531725\pi$
$710$		0			0
$711$		0			0
$712$			51.7394i			1.93902i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$719$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$720$	18.4515	+	15.9883i	0.687646	+	0.595849i
$721$	1.87216	−	13.0212i	0.0697230	−	0.484934i
$722$	25.7816	−	7.57017i	0.959493	−	0.281733i
$723$	−11.7676	+	10.1966i	−0.437640	+	0.379217i
$724$	−6.26965	−	9.75577i	−0.233010	−	0.362570i
$725$	−13.6160	+	8.75045i	−0.505684	+	0.324983i
$726$	−5.29680	−	6.11283i	−0.196583	−	0.226868i
$727$	14.1953	+	48.3448i	0.526476	+	1.79301i	0.605151	+	0.796111i	$0.293113\pi$
$727$	14.1953	+	48.3448i	0.526476	+	1.79301i	−0.0786754	+	0.996900i	$0.525069\pi$
$728$		0			0
$729$	8.82624	−	10.1860i	0.326898	−	0.377260i
$730$		0			0
$731$		0			0
$732$	1.61154	−	0.735964i	0.0595641	−	0.0272020i
$733$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$733$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$734$	29.2415	−	45.5007i	1.07932	−	1.67946i
$735$		−	6.63931i		−	0.244894i
$736$	3.72171	−	26.8728i	0.137184	−	0.990546i
$737$		0			0
$738$	−36.4960	−	23.4545i	−1.34343	−	0.863373i
$739$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$739$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	40.1174	+	34.7619i	1.47176	+	1.27529i	0.885049	+	0.465498i	$0.154125\pi$
$743$	40.1174	+	34.7619i	1.47176	+	1.27529i	0.586715	+	0.809793i	$0.300421\pi$
$744$		0			0
$745$	23.7132	−	6.96282i	0.868784	−	0.255098i
$746$		0			0
$747$	−20.7314	−	32.2587i	−0.758521	−	1.18028i
$748$		0			0
$749$	−10.6203	−	12.2565i	−0.388058	−	0.447843i
$750$	−2.31613	−	7.88803i	−0.0845733	−	0.288030i
$751$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$751$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$752$	31.8819	−	36.7937i	1.16261	−	1.34173i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−6.69681	+	0.962856i	−0.243561	+	0.0350187i
$757$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$757$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.391715	−	0.251740i	−0.0141996	−	0.00912556i	0.533522	−	0.845786i	$-0.320868\pi$
$761$	−0.391715	−	0.251740i	−0.0141996	−	0.00912556i	−0.547721	+	0.836661i	$0.684505\pi$
$762$	−2.35604	−	16.3866i	−0.0853503	−	0.593625i
$763$	9.40447	+	20.5929i	0.340465	+	0.745514i
$764$		0			0
$765$		0			0
$766$	−41.6238	−	36.0672i	−1.50393	−	1.30316i
$767$		0			0
$768$	7.98213	−	2.34376i	0.288030	−	0.0845733i
$769$	−26.4727	+	22.9387i	−0.954629	+	0.827191i	−0.985036	−	0.172347i	$-0.944865\pi$
$769$	−26.4727	+	22.9387i	−0.954629	+	0.827191i	0.0304075	+	0.999538i	$0.490319\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$773$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$774$	39.2193	+	5.63888i	1.40971	+	0.202685i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	17.1865	−	7.84882i	0.616167	−	0.281394i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	9.64355			0.344632
$784$	19.2162	+	12.3495i	0.686293	+	0.441054i
$785$		0			0
$786$		0			0
$787$	15.5593	−	52.9902i	0.554630	−	1.88890i	0.108071	−	0.994143i	$-0.465533\pi$
$787$	15.5593	−	52.9902i	0.554630	−	1.88890i	0.446560	−	0.894754i	$-0.352649\pi$
$788$		0			0
$789$	−10.2062	−	8.84373i	−0.363351	−	0.314845i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$797$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$798$		0			0
$799$		0			0
$800$	27.1386	+	7.96860i	0.959493	+	0.281733i
$801$	45.4204	−	20.7428i	1.60485	−	0.732910i
$802$	−32.0676	+	4.61063i	−1.13235	+	0.162807i
$803$		0			0
$804$			2.02701i			0.0714873i
$805$	1.79542	+	12.0440i	0.0632802	+	0.424496i
$806$		0			0
$807$	11.1751	+	7.18180i	0.393382	+	0.252811i
$808$	−2.53253	−	17.6141i	−0.0890939	−	0.619662i
$809$	14.8538	+	32.5252i	0.522230	+	1.14352i	0.968588	+	0.248670i	$0.0799935\pi$
$809$	14.8538	+	32.5252i	0.522230	+	1.14352i	−0.446358	+	0.894854i	$0.647279\pi$
$810$	5.91569	−	20.1470i	0.207856	−	0.707893i
$811$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$811$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$812$	5.55591	+	4.81422i	0.194974	+	0.168946i
$813$		0			0
$814$		0			0
$815$	25.0921	−	21.7424i	0.878937	−	0.761603i
$816$		0			0
$817$		0			0
$818$	6.94728	+	8.01759i	0.242906	+	0.280328i
$819$		0			0
$820$	−49.7469	−	7.15253i	−1.73724	−	0.249777i
$821$	−35.9357	+	41.4720i	−1.25416	+	1.44738i	−0.409300	+	0.912400i	$0.634227\pi$
$821$	−35.9357	+	41.4720i	−1.25416	+	1.44738i	−0.844863	+	0.534982i	$0.820318\pi$
$822$		0			0
$823$	−23.1899	−	6.80918i	−0.808351	−	0.237353i	−0.148658	−	0.988889i	$-0.547495\pi$
$823$	−23.1899	−	6.80918i	−0.808351	−	0.237353i	−0.659693	+	0.751536i	$0.729314\pi$
$824$	29.8063	−	13.6121i	1.03835	−	0.474200i
$825$		0			0
$826$		0			0
$827$		−	47.4342i		−	1.64945i	−0.565536	−	0.824724i	$-0.691331\pi$
$827$		−	47.4342i		−	1.64945i	0.565536	−	0.824724i	$-0.308669\pi$
$828$	−25.0828	+	7.50638i	−0.871689	+	0.260865i
$829$	−26.5328			−0.921521			−0.460760	−	0.887525i	$-0.652423\pi$
$829$	−26.5328			−0.921521			−0.460760	+	0.887525i	$0.652423\pi$
$830$	−37.3713	−	24.0171i	−1.29718	−	0.833645i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.29443	−	1.98814i	−0.0794022	−	0.0688024i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$839$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$840$	−3.14130	+	2.01879i	−0.108385	+	0.0696549i
$841$	12.1289	+	13.9975i	0.418239	+	0.482674i
$842$	−8.09277	−	27.5614i	−0.278895	−	0.949830i
$843$	12.3105	+	1.76999i	0.423998	+	0.0609616i
$844$		0			0
$845$	26.4420	+	12.0757i	0.909632	+	0.415415i
$846$	−45.0817	−	13.2372i	−1.54994	−	0.455103i
$847$	−11.3620	+	5.18884i	−0.390402	+	0.178291i
$848$		0			0
$849$	−8.25251	+	12.8412i	−0.283225	+	0.440707i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$853$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$854$	−0.389358	−	2.70804i	−0.0133235	−	0.0926673i
$855$		0			0
$856$	11.3809	−	38.7597i	0.388990	−	1.32478i
$857$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$857$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$858$		0			0
$859$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$859$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$860$	44.0429	−	12.9322i	1.50185	−	0.440983i
$861$	5.01447	−	4.34506i	0.170893	−	0.148079i
$862$		0			0
$863$	37.9744	−	24.4047i	1.29266	−	0.830745i	0.300272	−	0.953854i	$-0.402923\pi$
$863$	37.9744	−	24.4047i	1.29266	−	0.830745i	0.992393	+	0.123108i	$0.0392863\pi$
$864$	−11.0359	−	12.7362i	−0.375450	−	0.433293i
$865$		0			0
$866$		0			0
$867$	−5.78835	+	6.68011i	−0.196583	+	0.226868i
$868$		0			0
$869$		0			0
$870$	4.84143	−	2.21101i	0.164140	−	0.0749602i
$871$		0			0
$872$	−30.4867	+	47.4382i	−1.03241	+	1.60646i
$873$		0			0
$874$		0			0
$875$	−12.6955			−0.429187
$876$		0			0
$877$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$877$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.2297	+	13.1966i	0.513100	+	0.444604i	0.872524	−	0.488570i	$-0.162481\pi$
$881$	15.2297	+	13.1966i	0.513100	+	0.444604i	−0.359424	+	0.933174i	$0.617027\pi$
$882$	3.13729	−	21.8203i	0.105638	−	0.734728i
$883$	−56.0021	+	16.4437i	−1.88462	+	0.553375i	−0.889232	+	0.457456i	$0.848761\pi$
$883$	−56.0021	+	16.4437i	−1.88462	+	0.553375i	−0.995389	+	0.0959188i	$0.969421\pi$
$884$		0			0
$885$		0			0
$886$	−30.5359	+	19.6242i	−1.02587	+	0.659288i
$887$	38.9028	+	44.8963i	1.30623	+	1.50747i	0.708269	+	0.705943i	$0.249477\pi$
$887$	38.9028	+	44.8963i	1.30623	+	1.50747i	0.597960	+	0.801526i	$0.295978\pi$
$888$		0			0
$889$	−25.3054	−	3.63837i	−0.848716	−	0.122027i
$890$	37.8814	−	43.7174i	1.26979	−	1.46541i
$891$		0			0
$892$	−18.1549	−	5.33077i	−0.607872	−	0.178487i
$893$		0			0
$894$	−8.04436	+	1.15660i	−0.269044	+	0.0386827i
$895$		0			0
$896$		−	12.8470i		−	0.429187i
$897$		0			0
$898$	59.9262			1.99976
$899$		0			0
$900$	−3.88471	−	27.0187i	−0.129490	−	0.900625i
$901$		0			0
$902$		0			0
$903$	−2.51741	+	5.51236i	−0.0837742	+	0.183440i
$904$		0			0
$905$	−1.84518	+	12.8335i	−0.0613360	+	0.426601i
$906$		0			0
$907$	−36.4661	+	31.5980i	−1.21084	+	1.04920i	−0.213449	+	0.976954i	$0.568470\pi$
$907$	−36.4661	+	31.5980i	−1.21084	+	1.04920i	−0.997387	+	0.0722410i	$0.976985\pi$
$908$	26.5116	+	41.2528i	0.879817	+	1.36902i
$909$	−14.4475	+	9.28487i	−0.479195	+	0.307960i
$910$		0			0
$911$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$911$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−1.90051	−	0.558041i	−0.0628291	−	0.0184483i
$916$	−27.2967	+	12.4660i	−0.901907	+	0.411887i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−22.8198	+	19.9814i	−0.752346	+	0.658768i
$921$	12.2241			0.402799
$922$	−47.7887	−	30.7119i	−1.57384	−	1.01144i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	23.1490	−	50.6893i	0.760725	−	1.66575i
$927$	−23.8992	−	20.7088i	−0.784954	−	0.680166i
$928$	−2.60601	+	18.1252i	−0.0855466	+	0.594990i
$929$	−46.4406	+	13.6362i	−1.52367	+	0.447389i	−0.933105	−	0.359605i	$-0.882912\pi$
$929$	−46.4406	+	13.6362i	−1.52367	+	0.447389i	−0.590561	+	0.806993i	$0.701093\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−11.3395	−	38.6188i	−0.371040	−	1.26365i
$935$		0			0
$936$		0			0
$937$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$937$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$938$	3.00347	+	0.881897i	0.0980666	+	0.0287950i
$939$		0			0
$940$	−53.8774	+	7.74641i	−1.75729	+	0.252660i
$941$	10.6110	−	16.5110i	0.345907	−	0.538242i	−0.624092	−	0.781351i	$-0.714531\pi$
$941$	10.6110	−	16.5110i	0.345907	−	0.538242i	0.969999	+	0.243109i	$0.0781673\pi$
$942$		0			0
$943$	35.0830	−	40.9144i	1.14246	−	1.33236i
$944$		0			0
$945$	6.36346	+	4.08955i	0.207003	+	0.133033i
$946$		0			0
$947$	−23.3823	−	51.2001i	−0.759823	−	1.66378i	−0.747865	−	0.663851i	$-0.768921\pi$
$947$	−23.3823	−	51.2001i	−0.759823	−	1.66378i	−0.0119574	−	0.999929i	$-0.503806\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$953$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−8.46053	−	3.86379i	−0.273062	−	0.124703i
$961$	−29.7443	−	8.73371i	−0.959493	−	0.281733i
$962$		0			0
$963$	−38.5885	+	5.54819i	−1.24350	+	0.178788i
$964$	−32.3810	+	50.3858i	−1.04292	+	1.62282i
$965$		0			0
$966$	−0.0207496	−	4.00429i	−0.000667607	−	0.128836i
$967$	−61.4860			−1.97726			−0.988629	−	0.150377i	$-0.951951\pi$
$967$	−61.4860			−1.97726			−0.988629	+	0.150377i	$0.951951\pi$
$968$	−26.1737	−	16.8208i	−0.841254	−	0.540641i
$969$		0			0
$970$		0			0
$971$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$971$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$972$	−10.2938	+	22.5402i	−0.330173	+	0.722978i
$973$		0			0
$974$	−1.66562	+	11.5846i	−0.0533699	+	0.371196i
$975$		0			0
$976$	5.15022	−	4.46269i	0.164854	−	0.142847i
$977$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$977$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$978$	−9.18485	+	5.90275i	−0.293699	+	0.188749i
$979$		0			0
$980$	−7.19504	−	24.5040i	−0.229837	−	0.782753i
$981$	53.8669	+	7.74489i	1.71984	+	0.247275i
$982$		0			0
$983$	−16.1290	−	7.36585i	−0.514434	−	0.234934i	0.141244	−	0.989975i	$-0.454890\pi$
$983$	−16.1290	−	7.36585i	−0.514434	−	0.234934i	−0.655678	+	0.755041i	$0.727617\pi$
$984$	15.8576	+	4.65622i	0.505523	+	0.148435i
$985$		0			0
$986$		0			0
$987$	3.88505	−	6.04525i	0.123662	−	0.192422i
$988$		0			0
$989$	−13.6233	+	47.3020i	−0.433195	+	1.50412i
$990$		0			0
$991$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$991$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	11.0402	+	9.56636i	0.349821	+	0.303122i
$997$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$997$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.a.159.4	yes	40
4.3	odd	2	inner	460.2.o.a.159.1	✓	40
5.4	even	2	inner	460.2.o.a.159.1	✓	40
20.19	odd	2	CM	460.2.o.a.159.4	yes	40
23.11	odd	22	inner	460.2.o.a.379.4	yes	40
92.11	even	22	inner	460.2.o.a.379.1	yes	40
115.34	odd	22	inner	460.2.o.a.379.1	yes	40
460.379	even	22	inner	460.2.o.a.379.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.a.159.1	✓	40	4.3	odd	2	inner
460.2.o.a.159.1	✓	40	5.4	even	2	inner
460.2.o.a.159.4	yes	40	1.1	even	1	trivial
460.2.o.a.159.4	yes	40	20.19	odd	2	CM
460.2.o.a.379.1	yes	40	92.11	even	22	inner
460.2.o.a.379.1	yes	40	115.34	odd	22	inner
460.2.o.a.379.4	yes	40	23.11	odd	22	inner
460.2.o.a.379.4	yes	40	460.379	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18971 + 0.764582i) q^{2} +(0.0739958 + 0.514652i) q^{3} +(0.830830 + 1.81926i) q^{4} +(0.629973 - 2.14549i) q^{5} +(-0.305460 + 0.668863i) q^{6} +(0.858171 + 0.743609i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(2.61909 - 0.769034i) q^{9} +O(q^{10})\)	\(q+(1.18971 + 0.764582i) q^{2} +(0.0739958 + 0.514652i) q^{3} +(0.830830 + 1.81926i) q^{4} +(0.629973 - 2.14549i) q^{5} +(-0.305460 + 0.668863i) q^{6} +(0.858171 + 0.743609i) q^{7} +(-0.402527 + 2.79964i) q^{8} +(2.61909 - 0.769034i) q^{9} +(2.38989 - 2.07085i) q^{10} +(-0.874810 + 0.562206i) q^{12} +(0.452426 + 1.54082i) q^{14} +(1.15080 + 0.165460i) q^{15} +(-2.61944 + 3.02300i) q^{16} +(3.70395 + 1.08758i) q^{18} +(4.42662 - 0.636451i) q^{20} +(-0.319199 + 0.496683i) q^{21} +(-1.96963 + 4.37271i) q^{23} -1.47062 q^{24} +(-4.20627 - 2.70320i) q^{25} +(1.23756 + 2.70989i) q^{27} +(-0.639827 + 2.17905i) q^{28} +(1.34473 - 2.94454i) q^{29} +(1.24261 + 1.07673i) q^{30} +(-5.42771 + 1.59372i) q^{32} +(2.13603 - 1.37274i) q^{35} +(3.57509 + 4.12588i) q^{36} +(5.75302 + 2.62732i) q^{40} +(-10.7829 - 3.16615i) q^{41} +(-0.759509 + 0.346856i) q^{42} +(10.1596 - 1.46073i) q^{43} -6.10370i q^{45} +(-5.68658 + 3.69632i) q^{46} -12.1712 q^{47} +(-1.74962 - 1.12441i) q^{48} +(-0.812702 - 5.65246i) q^{49} +(-2.93743 - 6.43207i) q^{50} +(-0.599585 + 4.17020i) q^{54} +(-2.42727 + 2.10324i) q^{56} +(3.85118 - 2.47500i) q^{58} +(0.655102 + 2.23107i) q^{60} +(-1.68634 - 0.242459i) q^{61} +(2.81948 + 1.28762i) q^{63} +(-7.67594 - 2.25386i) q^{64} +(1.05385 - 1.63982i) q^{67} +(-2.39617 - 0.690111i) q^{69} +3.59084 q^{70} +(1.09876 + 7.64205i) q^{72} +(1.07996 - 2.36479i) q^{75} +(4.83564 + 7.52440i) q^{80} +(5.58593 - 3.58986i) q^{81} +(-10.4078 - 12.0112i) q^{82} +(-3.95775 - 13.4789i) q^{83} +(-1.16880 - 0.168048i) q^{84} +(13.2038 + 6.02999i) q^{86} +(1.61492 + 0.474182i) q^{87} +(18.1065 - 2.60331i) q^{89} +(4.66678 - 7.26165i) q^{90} +(-9.59153 + 0.0497018i) q^{92} +(-14.4803 - 9.30591i) q^{94} +(-1.22184 - 2.67545i) q^{96} +(3.35489 - 7.34618i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more